A138940 Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.

2, 4, 10, 12, 14, 19, 23, 24, 36, 38, 39, 48, 62, 93, 106, 120, 134, 150, 196, 317, 320, 385, 586, 597, 654, 738, 945, 1031, 1172, 1282, 1404, 1426, 1452, 1521, 1752, 1812, 1836, 1844, 1862, 2134, 2232, 2264, 2667, 3750, 3903, 3927, 4274, 4354, 5877, 6022

Offset: 1

Author

M. F. Hasler, Apr 03 2008

Keywords

• nonn

Comments

Unique period primes (A040017) are often of the form Phi(k,10) or Phi(k,-10).

Terms of this sequence which are the square of a prime, a(n)=p^2, are such that A252491(p) is prime. Apart from a(2)=2^2, there is no such term up to 26570. - M. F. Hasler, Jan 09 2015

Links

• Ray Chandler, Table of n, a(n) for n = 1..102 (first 50 terms from Robert Price, terms 92-93 from Serge Batalov, others from Kamada link)
• Chris Caldwell, Unique Primes.
• Makoto Kamada, Factorizations of Phi_n(10) (including prime members up to 200000).
• Index entries for cyclotomic polynomials, values at X

Crossrefs

Cf. A019328, A040017, A085035, A252491.

Cf. Subsequence of A007498, contains A004023.

Programs

Mathematica

Select[Range[1000], PrimeQ[Cyclotomic[#, 10]] &] (* T. D. Noe, Mar 03 2012 *)

PARI

for( i=1,999, isprime( polcyclo(i,10)) && print1( i","))

Extensions

a(28)-a(43) from Robert Price, Mar 03 2012

a(44)-a(50) from Robert Price, Apr 14 2012

a(51)-a(91) from Ray Chandler, Maksym Voznyy et al. (cf. Phi_n(10) link), ca. 2009

a(92)-a(93) from Serge Batalov, Mar 28 2015